Temperature change of ice water

[kmarlow123]

A tub of icy water at 0 degrees C hold 100 gallons. You put a 25 pound watermelon with a temperature of 29.4 degrees C. The tub is wrapped in blankets to avoid heat loss. What will be the final temperature of the watermelon, considering that a watermelon is mostly water?

 

[NobodySpecial]

Would you like to make some sort of attempt at the answer?

 

[kmarlow123]

I am attempting to help my nephew with the problem but I can't remember how to go about setting up a problem like this, I don't need the answer, just some help on setting it up.

 

[NobodySpecial]

Sorry - there is a homework forum which puts up a template to fill in what you have done so far. There is no point in us just supplying answers to homework questions

There is an equation linking the amount of energy to the temperature change
Q = mcT, where c is the specific heat capacity of water

The energy lost by the watermelon = the energy gained by the water.

 

[rwisz]

The final temperature of the watermelon will depend on a few factors, such as the specific heat capacity of the watermelon and the thermal conductivity of the blankets. However, we can make some estimations based on the information given.

First, we know that the watermelon has a temperature of 29.4 degrees C, which is significantly higher than the temperature of the ice water (0 degrees C). This means that heat will flow from the watermelon to the ice water, causing the watermelon to cool down and the ice water to warm up.

Next, the mass of the watermelon (25 pounds) is relatively small compared to the mass of the ice water (100 gallons). This means that the watermelon will have a smaller effect on the overall temperature of the ice water.

Assuming that the blankets are effective in preventing heat loss, the watermelon will eventually reach a temperature that is close to the temperature of the ice water. This is because the watermelon and the ice water will reach a thermal equilibrium, where they are both at the same temperature.

Based on these factors, I would estimate that the final temperature of the watermelon will be slightly above 0 degrees C, but significantly lower than its initial temperature of 29.4 degrees C. This is because the watermelon will lose heat to the ice water, but it will also gain some heat from the surrounding environment through the blankets. Overall, the final temperature of the watermelon will likely be close to the temperature of the ice water, but not exactly the same.